Inverse positivity for general Robin problems on Lipschitz domains
It is proved that elliptic boundary value problems in divergence form can be written in many equivalent forms. This is used to prove regularity properties and maximum principles for problems with Robin boundary conditions with negative or indefinite boundary coefficient on Lipschitz domains by rewriting them as a problem with positive coefficient. It is also shown that such methods cannot be applied to domains with an outward pointing cusp. Applications to the regularity of the harmonic Steklov eigenfunctions on Lipschitz domains are given.
Mathematics Subject Classification (2000).35J25 35B50 35B65
Keywords.Elliptic boundary value problems Robin problems Lp-estimates maximum priciple Steklov eigenfunctions
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